Struct HeatEquationSolver 

pub struct HeatEquationSolver { /* private fields */ }

Heat equation solver implementing PDESolver trait

Implementations

impl HeatEquationSolver

pub fn new() -> Self

Creates a new heat equation solver

pub fn with_max_terms(max_terms: usize) -> Self

Creates solver with custom maximum number of terms

pub fn solve_heat_equation_1d( &self, pde: &Pde, alpha: &Expression, boundary_conditions: &[BoundaryCondition], _initial_condition: &InitialCondition, ) -> PDEResult

Solves the 1D heat equation with full Fourier series computation

Arguments

• pde - The heat equation PDE
• alpha - Thermal diffusivity coefficient
• boundary_conditions - Boundary conditions
• _initial_condition - Initial temperature distribution (currently unused)

Returns

A PDESolution containing the heat equation solution with eigenvalues and symbolic Fourier coefficients.

Errors

Returns PDEError::InvalidForm if the PDE does not have exactly 2 independent variables (x and t for 1D heat equation).

Mathematical Background

Solution form: u(x,t) = sum A_n sin(sqrt(lambda_n) x) exp(-lambda_n alpha t) where lambda_n are eigenvalues determined by boundary conditions and A_n are Fourier coefficients determined by initial condition.

Trait Implementations

impl Default for HeatEquationSolver

fn default() -> Self

Returns the “default value” for a type.

impl PDESolver for HeatEquationSolver

fn solve(&self, pde: &Pde) -> PDEResult

Attempts to solve the given PDE

fn can_solve(&self, pde_type: PdeType) -> bool

Returns true if this solver can handle the given PDE type

fn priority(&self) -> u8

Priority for this solver (higher = try first)

fn name(&self) -> &'static str

Solver name for diagnostics

fn description(&self) -> &'static str

Solver description